Large language models (LLMs) have achieved significant performance improvements in natural language processing (NLP) domain. However, these models often require large computational resources for training and inference. Recently, Mamba, a language model architecture based on State-Space Models (SSMs), has achieved comparable performance to Transformer models while significantly reducing costs by compressing context windows during inference. We focused on the potential of the lightweight Mamba architecture by applying BitNet quantization method to the model architecture. In addition, while prior BitNet methods generally quantized only linear layers in the main body, we extensively quantized the embedding and projection layers considering their significant proportion of model parameters. In our experiments, we applied ternary quantization to the Mamba-2 (170M) architecture and pre-trained the model with 150 B tokens from scratch. Our method achieves approximately 90.0% reduction in the bits used by all parameters, achieving a significant improvement compared with a 48.4% reduction by the conventional BitNet quantization method. In addition, our method experienced minimal performance degradation in both the pre-training perplexity and downstream tasks. These findings demonstrate the potential of incorporating lightweight language models into edge devices, which will become more demanding in the future.